Princeton University

Let \[ f(t)=\sum_{N n 2N}a_nn^{-it} \] be a Dirichlet polynomial. We consider the weighted square mean value \[ I=\int_{-\infty}^{\infty}|f(t)|^2\exp\{-\Delta^{-2}(t-T)^2\}\,dt, \] where \(T\) is a large paremeter and \[ \Delta = \frac{T}{\log T}...

The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear polynomials. One can...

Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the...

Embedded contact homology is an invariant of a contact three-manifold, which is recently shown to be isomorphic to Heegaard Floer homology and Seiberg-Witten Floer homology. However, ECH chain complex depends on the contact form on the manifold and...

Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of Juhász in Heegaard Floer homology. In this talk, I will construct an invariant of a contact structure on a 3-manifold with...

Ideas of Kontsevich-Soibelman and Fukaya indicate that there is a natural rigid analytic space (the mirror) associated to a symplectic manifold equipped with a Lagrangian torus fibration. I will explain a construction which associates to a...

The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture...

In this talk I will explain how the heuristic arguments sketched in literature since 1999 fail to define a homology theory. These issues will be made clear with concrete examples and we will explore what stronger conditions are necessary to develop...

In this lecture, Alexander Nagel, Professor of Fine Arts at the Institute of Fine Arts at New York University, illustrates some ways in which art produced during the Renaissance period points ­eastward towards Constantinople, towards the Holy Land...